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1. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter ; Zeitlin, Anton M. ( September 2023 , Communications in Mathematical Physics)

   We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$$C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$$C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$$X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$$l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$$ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$$P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual.

    

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2. On the sensitivity reach of $$\textrm{LQ}$$ production with preferential couplings to third generation fermions at the LHC

   https://doi.org/10.1140/epjc/s10052-023-12177-4  

   Flórez, A. ; Jones-Pérez, J. ; Gurrola, A. ; Rodriguez, C. ; Peñuela-Parra, J. ( November 2023 , The European Physical Journal C)

   Leptoquarks ($$\textrm{LQ}$$$\text{LQ}$s) are hypothetical particles that appear in various extensions of the Standard Model (SM), that can explain observed differences between SM theory predictions and experimental results. The production of these particles has been widely studied at various experiments, most recently at the Large Hadron Collider (LHC), and stringent bounds have been placed on their masses and couplings, assuming the simplest beyond-SM (BSM) hypotheses. However, the limits are significantly weaker for$$\textrm{LQ}$$$\text{LQ}$models with family non-universal couplings containing enhanced couplings to third-generation fermions. We present a new study on the production of a$$\textrm{LQ}$$$\text{LQ}$at the LHC, with preferential couplings to third-generation fermions, considering proton-proton collisions at$$\sqrt{s} = 13 \, \textrm{TeV}$$$\sqrt{s}=13\text{TeV}$and$$\sqrt{s} = 13.6 \, \textrm{TeV}$$$\sqrt{s}=13.6\text{TeV}$. Such a hypothesis is well motivated theoretically and it can explain the recent anomalies in the precision measurements of$$\textrm{B}$$$\text{B}$-meson decay rates, specifically the$$R_{D^{(*)}}$$$R_{D^{(\ast )}}$ratios. Under a simplified model where the$$\textrm{LQ}$$$\text{LQ}$masses and couplings are free parameters, we focus on cases where the$$\textrm{LQ}$$$\text{LQ}$decays to a$$\tau $$$\tau$lepton and a$$\textrm{b}$$$\text{b}$quark, and study how the results are affected by different assumptions about chiral currents and interference effects with other BSM processes with the same final states, such as diagrams with a heavy vector boson,$$\textrm{Z}^{\prime }$$${\text{Z}}^{\prime }$. The analysis is performed using machine learning techniques, resulting in an increased discovery reach at the LHC, allowing us to probe new physics phase space which addresses the$$\textrm{B}$$$\text{B}$-meson anomalies, for$$\textrm{LQ}$$$\text{LQ}$masses up to$$5.00\, \textrm{TeV}$$$5.00\text{TeV}$, for the high luminosity LHC scenario.

    

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3. Softmax policy gradient methods can take exponential time to converge

   https://doi.org/10.1007/s10107-022-01920-6  

   Li, Gen ; Wei, Yuting ; Chi, Yuejie ; Chen, Yuxin ( January 2023 , Mathematical Programming)

   The softmax policy gradient (PG) method, which performs gradient ascent under softmax policy parameterization, is arguably one of the de facto implementations of policy optimization in modern reinforcement learning. For$$\gamma $$$\gamma$-discounted infinite-horizon tabular Markov decision processes (MDPs), remarkable progress has recently been achieved towards establishing global convergence of softmax PG methods in finding a near-optimal policy. However, prior results fall short of delineating clear dependencies of convergence rates on salient parameters such as the cardinality of the state space$${\mathcal {S}}$$$S$and the effective horizon$$\frac{1}{1-\gamma }$$$\frac{1}{1-\gamma }$, both of which could be excessively large. In this paper, we deliver a pessimistic message regarding the iteration complexity of softmax PG methods, despite assuming access to exact gradient computation. Specifically, we demonstrate that the softmax PG method with stepsize$$\eta $$$\eta$can take$$\begin{aligned} \frac{1}{\eta } |{\mathcal {S}}|^{2^{\Omega \big (\frac{1}{1-\gamma }\big )}} ~\text {iterations} \end{aligned}$$$\begin{array}{c}\frac{1}{\eta }{\left|S\right|}^{2^{\Omega (\frac{1}{1-\gamma })}}\text{iterations}\end{array}$to converge, even in the presence of a benign policy initialization and an initial state distribution amenable to exploration (so that the distribution mismatch coefficient is not exceedingly large). This is accomplished by characterizing the algorithmic dynamics over a carefully-constructed MDP containing only three actions. Our exponential lower bound hints at the necessity of carefully adjusting update rules or enforcing proper regularization in accelerating PG methods.

    

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4. Search for light Higgs bosons from supersymmetric cascade decays in $$\text {pp}$$ collisions at $$\sqrt{s}=13\,\textrm{TeV}$$

   https://doi.org/10.1140/epjc/s10052-023-11581-0  

   Tumasyan, A. ; Adam, W. ; Andrejkovic, J. W. ; Bergauer, T. ; Chatterjee, S. ; Damanakis, K. ; Dragicevic, M. ; Valle, A. Escalante ; Frühwirth, R. ; Jeitler, M. ; et al ( July 2023 , The European Physical Journal C)

   A search is reported for pairs of light Higgs bosons ($${\textrm{H}} _1$$${\text{H}}_1$) produced in supersymmetric cascade decays in final states with small missing transverse momentum. A data set of LHC$$\hbox {pp}$$$\text{pp}$collisions collected with the CMS detector at$$\sqrt{s}=13\,\text {TeV} $$$\sqrt{s}=13\text{TeV}$and corresponding to an integrated luminosity of 138$$\,\text {fb}^{-1}$$${\text{fb}}^{-1}$is used. The search targets events where both$${\textrm{H}} _1$$${\text{H}}_1$bosons decay into Equation missing<#comment/>pairs that are reconstructed as large-radius jets using substructure techniques. No evidence is found for an excess of events beyond the background expectations of the standard model (SM). Results from the search are interpreted in the next-to-minimal supersymmetric extension of the SM, where a “singlino” of small mass leads to squark and gluino cascade decays that can predominantly end in a highly Lorentz-boosted singlet-like$${\textrm{H}} _1$$${\text{H}}_1$and a singlino-like neutralino of small transverse momentum. Upper limits are set on the product of the squark or gluino pair production cross section and the square of the Equation missing<#comment/>branching fraction of the$${\textrm{H}} _1$$${\text{H}}_1$in a benchmark model containing almost mass-degenerate gluinos and light-flavour squarks. Under the assumption of an SM-like Equation missing<#comment/>branching fraction,$${\textrm{H}} _1$$${\text{H}}_1$bosons with masses in the range 40–120$$\,\text {GeV}$$$\text{GeV}$arising from the decays of squarks or gluinos with a mass of 1200–2500$$\,\text {GeV}$$$\text{GeV}$are excluded at 95% confidence level.

    

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5. Borexino’s search for low-energy neutrinos associated with gravitational wave events from GWTC-3 database: Borexino Collaboration

   https://doi.org/10.1140/epjc/s10052-023-11688-4  

   Basilico, D. ; Bellini, G. ; Benziger, J. ; Biondi, R. ; Caccianiga, B. ; Calaprice, F. ; Caminata, A. ; Chepurnov, A. ; D’Angelo, D. ; Derbin, A. ; et al ( June 2023 , The European Physical Journal C)

   The search for neutrino events in correlation with gravitational wave (GW) events for three observing runs (O1, O2 and O3) from 09/2015 to 03/2020 has been performed using the Borexino data-set of the same period. We have searched for signals of neutrino-electron scattering and inverse beta-decay (IBD) within a time window of$$\pm \, 1000$$$\pm 1000$ s centered at the detection moment of a particular GW event. The search was done with three visible energy thresholds of 0.25, 0.8 and 3.0 MeV. Two types of incoming neutrino spectra were considered: the mono-energetic line and the supernova-like spectrum. GW candidates originated by merging binaries of black holes (BHBH), neutron stars (NSNS) and neutron star and black hole (NSBH) were analyzed separately. Additionally, the subset of most intensive BHBH mergers at closer distances and with larger radiative mass than the rest was considered. In total, follow-ups of 74 out of 93 gravitational waves reported in the GWTC-3 catalog were analyzed and no statistically significant excess over the background was observed. As a result, the strongest upper limits on GW-associated neutrino and antineutrino fluences for all flavors ($$\nu _e, \nu _\mu , \nu _\tau $$${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$) at the level$$10^9{-}10^{15}~\textrm{cm}^{-2}\,\textrm{GW}^{-1}$$${10}^9-{10}^{15}{\text{cm}}^{-2}{\text{GW}}^{-1}$have been obtained in the 0.5–5 MeV neutrino energy range.

    

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